Similar and Congruent Triangles
-know the three ways of proving relationships between triangles
-know how to state proportional sides
Keys Ideas on p457 goes over all the main concepts.
Example 3 on p459 have two good examples.
Remember if you have two sides of a right angle triangle you can find the third using Pythagorean Theorem.
HW p461 #4, 6, 7 (try them all, but don't worry if some are too hard)
5.2 Scale Factor
-know how to calculate scale factor
-know typical problems of measuring tree, and measuring across a gorge.
-remember Pythagorean theorem and use when necessary.
-be able to do ladder problem
Example 2 on p472 is typical.
HW. p475 #7, 8
5.3 Slope Angles
Slope Angle
-use tan to calculate angle, and tan inverse to calculate slope when given an angle.
-understand terms - angle of inclination and elevation
-angle of declination and depression
See hand out
p486 #4,5, 6, 8, 10
Unit 5
5.4 Primary Trigonometric Ratios
Key ideas are on p493
Note the ratios only work for right angle triangles.
The hypotenuse is always opposite the right angle.
Memorize the three primary trig ratios. Some students use SOH-CAH-TOA as an aid to memorization. It is pronounced "so - ka - toe - ah".
The SOH stands for "Sine of an angle is Opposite over Hypotenuse."
The CAH stands for "Cosine of an angle is Adjacent over Hypotenuse."
The TOA stands for "Tangent of an angle is Opposite over Adjacent."
HW: p. 496 # 4,5,6, 9, 10, 11
5.5 Applications
Types of Questions.
1. Searchlight beam question on page 503.
use tan 72.5 = 150/x1 and tan 67.5 = 150/x2
answer is about 15m.
2. Area of a Triangle p 505
3. Example 2 p507 looking out from a window.
HW.
Review Topics
Similar and Congruent triangles (gorge problem) (scale factor)
SSS, SAS, AA
Slope Angle (relating tangent to slope, find equation of line)
Primary Trig Ratios, find unknown sides and angles of 90o triangle
Non-Right angle triangles
Sine Law - when we know angle and opposite side
Cosine Law - when we know two sides and a contained angle
-or when we know all three sides.
Remember
24-20x is not 4x,
so
500-400cos20 is not 100cos20. Calculator will use BEDMAS and be correct.
1. Area of a triangle
2. Height of flagpole type question
3. Golf question and/or looking down at two boats type question.
4. Two planes taking off from the same point type question
5. Similar triangles involving ladders
Similar triangle to measure gorge
Similar triangle to measure tree when Susan is in shadow
Know theorems from Grade 9. OAT, PLT F, Z patterns.
Pythagorean Theorems.
HW. q15, 16, 18, and find area of q15 from review handout
5.1 Congruent and Similar Triangles
Similar and Congruent Triangles-know the three ways of proving relationships between triangles
-know how to state proportional sides
Keys Ideas on p457 goes over all the main concepts.
Example 3 on p459 have two good examples.
Remember if you have two sides of a right angle triangle you can find the third using Pythagorean Theorem.
HW p461 #4, 6, 7 (try them all, but don't worry if some are too hard)
5.2 Scale Factor
-know how to calculate scale factor
-know typical problems of measuring tree, and measuring across a gorge.
-remember Pythagorean theorem and use when necessary.
-be able to do ladder problem
Example 2 on p472 is typical.
HW. p475 #7, 8
5.3 Slope Angles
Slope Angle
-use tan to calculate angle, and tan inverse to calculate slope when given an angle.
-understand terms - angle of inclination and elevation
-angle of declination and depression
See hand out
p486 #4,5, 6, 8, 10
Unit 5
5.4 Primary Trigonometric Ratios
Key ideas are on p493
Note the ratios only work for right angle triangles.
The hypotenuse is always opposite the right angle.
Memorize the three primary trig ratios. Some students use SOH-CAH-TOA as an aid to memorization.
It is pronounced "so - ka - toe - ah".
The SOH stands for "Sine of an angle is Opposite over Hypotenuse."
The CAH stands for "Cosine of an angle is Adjacent over Hypotenuse."
The TOA stands for "Tangent of an angle is Opposite over Adjacent."
HW: p. 496 # 4,5,6, 9, 10, 11
5.5 Applications
Types of Questions.
1. Searchlight beam question on page 503.
use tan 72.5 = 150/x1 and tan 67.5 = 150/x2
answer is about 15m.
2. Area of a Triangle p 505
3. Example 2 p507 looking out from a window.
HW.
Review Topics
Similar and Congruent triangles (gorge problem) (scale factor)
SSS, SAS, AA
Slope Angle (relating tangent to slope, find equation of line)
Primary Trig Ratios, find unknown sides and angles of 90o triangle
Non-Right angle triangles
Sine Law - when we know angle and opposite side
Cosine Law - when we know two sides and a contained angle
-or when we know all three sides.
Remember
24-20x is not 4x,
so
500-400cos20 is not 100cos20. Calculator will use BEDMAS and be correct.
Review Questions
p512 #3, 10
p515 1a, 2ac
p518 3c, 5
p523 13
p524 17, 18
p586 3,4,5,6
Unit Test will application questions like
1. Area of a triangle2. Height of flagpole type question
3. Golf question and/or looking down at two boats type question.
4. Two planes taking off from the same point type question
5. Similar triangles involving ladders
Similar triangle to measure gorge
Similar triangle to measure tree when Susan is in shadow
Know theorems from Grade 9. OAT, PLT F, Z patterns.
Pythagorean Theorems.
HW. q15, 16, 18, and find area of q15 from review handout